\[\boxed{\mathbf{788\ (788).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \frac{60}{x} - \frac{60}{x + 10} = \frac{1}{5}\]
\[\frac{60}{x} - \frac{60}{x + 10} - \frac{1}{5} = 0;\ \ \ \ \ x \neq 0;\ \ \ \]
\[x \neq 5\]
\[- x^{2} - 10x + 300 = 0\]
\[x^{2} + 10x - 300 = 0\]
\[x_{1} + x_{2} = - 10,\ \ \]
\[x_{1}x_{2} = - 3000,\]
\[\text{\ \ }x_{1} = 50,\ \ x_{2} = - 60\]
\[Ответ:\ x = 50,\ x = - 60.\]
\[2)\ \frac{x}{x + 2} + \frac{x + 2}{x - 2} = \frac{16}{x^{2} - 4}\]
\[x^{2} - 2x + x^{2} + 4x + 4 - 16 = 0\]
\[x^{2} + x - 6 = 0\]
\[x_{1} + x_{2} = - 1,\ \ x_{1}x_{2} = - 6,\ \ \]
\[x_{1} = - 3,\ \ \]
\[x_{2} = 2\ (не\ подходит)\]
\[Ответ:\ x = - 3.\]
\[3)\ \frac{9}{x + 3} + \frac{14}{x - 3} = \frac{24}{x}\]
\[\ \frac{9}{x + 3} + \frac{14}{x - 3} - \frac{24}{x} = 0;\ \ \ \ x \neq 0;\]
\[x \neq 3;\ \ \ x \neq - 3\]
\[- x^{2} + 15x + 216 = 0\]
\[x^{2} - 15x - 216 = 0\]
\[x_{1} + x_{2} = 15,\ \ x_{1}x_{2} = - 216,\ \]
\[\ x_{1} = 24,\ \ x_{2} = - 9\]
\[Ответ:\ x = - 9;x = 24.\]
\[4)\ \frac{2y + 3}{2y + 2} - \frac{y + 1}{2y - 2} + \frac{1}{y^{2} - 1} = 0\]
\[y^{2} - y - 2 = 0\]
\[y_{1} + y_{2} = 1,\ \ y_{1}y_{2} = - 2,\]
\[\text{\ \ }y_{1} = 2,\ \ \]
\[y_{2} = - 1\ (не\ подходит)\]
\[Ответ:y = 2.\]
\[5)\ \frac{3x}{x^{2} - 10x + 25} - \frac{x - 3}{x^{2} - 5x} = \frac{1}{x}\]
\[\frac{3x}{(x - 5)^{2}} - \frac{x - 3}{x(x - 5)} - \frac{1}{x} = 0;\ \ \ \ \]
\[x \neq 0;\ \ x \neq 5\]
\[x^{2} + 18x - 40 = 0\]
\[x_{1} + x_{2} = - 18,\ \ x_{1}x_{2} = - 40,\ \]
\[\ x_{1} = 2,\ \ x_{2} = - 20\]
\[Ответ:\ x = - 20;x = 2.\]
\[x^{2} - 25x + 150 = 0\]
\[x_{1} + x_{2} = 25,\ \ x_{1}x_{2} = 150,\ \]
\[\ x_{1} = 10\ (не\ подходит),\ \ \]
\[x_{2} = 15\]
\[Ответ:x = 15.\]
\[\boxed{\mathbf{7}\mathbf{8}\mathbf{8}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ x² - x - 12 = 0\]
\[x_{1} + x_{2} = 1,\ \ x_{1} = 4\]
\[x_{1} \cdot x_{2} = - 12,\ \ x_{2} = - 3\]
\[x_{1} + x_{2} = - 5;\ \ \ \ x_{1} \cdot x_{2} = - 16\]
\[2)\ x² + 2x - 35 = 0\]
\[x_{1} + x_{2} = - 2,\ \ x_{1} = - 7\]
\[x_{1} \cdot x_{2} = - 35,\ \ x_{2} = 5\]
\[x_{1} + x_{2} = - 5;\ \ \ \ x_{1} \cdot x_{2} = - 16\]
\[3)\ 3x² - 16x + 5 = 0\]
\[D = 256 - 4 \cdot 3 \cdot 5 = 196\]
\[x = \frac{16 \pm 14}{6}\]
\[x_{1} = 5;\ \ \ \ x_{2} = \frac{1}{3}\]
\[Ответ:\ x = 5;\ \ x = \frac{1}{3}.\]
\[4)\ 16x² - 24x + 3 = 0\]
\[D = 576 - 4 \cdot 3 \cdot 16 = 384\]
\[x = \frac{24 \pm 8\sqrt{6}}{32} = \frac{3 \pm \sqrt{6}}{4}\]
\[x_{1} = \frac{3 + \sqrt{6}}{4};\ \ \ \ \ \ \ \ x_{2} = \frac{3 - \sqrt{6}}{4}\]
\[x_{1} + x_{2} = - 5;\ \ \ \ x_{1} \cdot x_{2} = - 16\]
\[5)\ 4x² + 28x + 49 = 0\]
\[D = 784 - 4 \cdot 4 \cdot 49 = 0\]
\[x = - \frac{28}{8} = - 3,5\]
\[x_{1} + x_{2} = - 5;\ \ \ \ x_{1} \cdot x_{2} = - 16\]
\[6)\ 3x² + 21x - 90 = 0\]
\[D = 441 + 4 \cdot 3 \cdot 90 = 1521\]
\[x = \frac{- 21 \pm 39}{6}\]
\(x_{1} = - 10\); \(x_{2} = 3\)
\[x_{1} + x_{2} = - 5;\ \ \ \ x_{1} \cdot x_{2} = - 16\]